The search for audio signal processing techniques and sound systems that can reproduce sound with higher quality continues in the modern age. An original, high quality audio signal often becomes degraded due to manipulations applied to it for purposes of storage and transmission. The problem of poor quality sound during playback is especially acute when the original audio signal has undergone lossy compression to reduce its bit rate, for purposes of either reduced storage requirements or to meet reduced transmission bandwidth over the Internet.
The quality of an encoded and then decoded (codec processed) audio signal may be improved by digital signal processing of the codec-processed signal, seeking to harmonically enhance and frequency equalize the signal. A digital filter can be designed to reshape the phase and frequency content of the codec processed audio signal that is passed through it, in hopes of recovering the lost realism (as experienced during its playback.) In another approach, the use of an all-pass filter has been suggested, which is a signal-processing block that passes all frequencies equally in terms of gain or magnitude, but changes the phase relationship between various frequencies. In an all-pass filter, the phase shift between the output and the input varies as a function of frequency. An all-pass filter may be described by the frequency at which its phase shift crosses 90° or when the input and output signals are described as going into quadrature or when there is a quarter wavelength of delay between the output and the input. All-pass filters are often used to compensate for undesired phase shifts that have arisen in an audio system. An all-pass filter may be implemented in a myriad of ways, as a digital infinite impulse response (IIR) filter whose difference equation has the well-known general form
      y    ⁡          (      n      )        =                    ∑                  i          =          0                N            ⁢                        a          i                ⁢                  x          ⁡                      (                          n              -              i                        )                                -                  ∑                  i          =          1                N            ⁢                        b          i                ⁢                  y          ⁡                      (                          n              -              i                        )                              
The efficacy of any codec-processed audio signal enhancement technique may be judged by comparing the spectral content of the enhanced audio signal to the original audio signal, or it may be judged in view of the improvement in how the enhanced audio signal sounds during playback.